The first step of an empirical analysis of the large deviations of
the time average of an observable is to determine the minimum length
of the averaging period \(T\)  for which the convergence to the large
deviation limit is satisfied up to an acceptable degree of accuracy.
The second step is to determine if the data available are enough to
study the non Gaussian tails of the rate function for the chosen range
of values of \(T\) . [1]} have recently provided a
systematic analysis of the convergence of statistical estimators of
large deviation functions of sums of independent and identically distributed
random variables, including a detailed study of the maximum range
of fluctuations for which the rate functions can be computed, given
a finite sample of data. These results in principle could be used,
with some additional considerations, to analyse the large fluctuations of the time averages
of an observable from time series of a dynamical process [1]},
and could therefore be of interest to perform precise large deviation
analysis of climatic observables.
